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Basic Algebra

Algebra : Simplify

Simplify y2 /X2 - 4y2 + y/2x + 4y When I have 2 after the y and the x it means squared. These are fractions, in case it is not clear.

Exponential and Logarithmic Functions

Endangered Species: A conservation organization releases 100 animals of an endangered species into a game preserve. The organization believes that the preserve has a carrying capacity of 1000 animals and that the growth of the herd will follow the logistic curve. p(t)=1000/1+9e^-0.1656t where t is measured in months (a)

Exponential and Logarithmic Functions

Radioactive Decay: Carbon 14 dating assumes that the carbon dioxide on earth today has the same radioactive content as it did centuries ago. If this is true, the amount of carbon 14 absorbed by a tree that grew several centuries ago should be the same as the amount of carbon 14 absorbed by a tree growing today. A peice of anc

Exponential and Logarithmic Equations : Modeling

The number of trees per acre N of a certain species is approximated by the model N=68(10^-0.04x), 5 <_ x <_ 40 (<_ = less than or = to) Where x is the average diameter of the trees (in inches) three feet above the ground. Use the model to approximate the average diameter of the trees in a test plot when N=21.

Describe the Nonabelian Group

Let G be a finite nonabelian group of order 27 where all the elements have order 3. Prove that there is exactly one such group G and give a complete description.

Irreducible Polynomial over a Field

Please see the attached file for the fully formatted problems. 5. Find an irreducible polynomial f(x) over the field Z3 with Z3[x]/(f(x)) = F243. Note that 243 = 3^5 . Please explain your reasoning and solution in as much detail as possible. Thank You.

Exponential & Logarithmic Functions Word Problem

NUMBER OF FARMS. The number N of farms in the United States has declined continually since 1950. In 1950 there were 5,647,800 farms, and in 1995 that number had decreased to 2,071,520. Assuming that the number of farms decreased according to the exponential model: A). Find the value of k, and write an exponential function

Finite Fields : Field Extensions

Please see the attached file for the fully formatted problem. Show the existence of an extension of Fq of order l for any prime l.

Quadratic Equations : Discriminants and Solving

For the equation 24x^2 + 68x + 28 = 0 a) Find the discriminant b) If the discriminant tells you that you can factor, do so. c) Solve the equation by completing the square(HINT: at some point during the process, you will come to a point which looks like (x+(17/12))^2 = (121/144) d) solve the equation by using the quadrati

Quadratic Equation : Proof by Completing the Square

1. Prove the Quadratic Formula by completing the square on ax^2+bx+c=0 2. A picture that is 14 in by 20 in is to have an even border. If the area of the picture and the border is 352 in^2, how wide will the border be?

Simplify the Expression

Please see the attached file for the fully formatted problems. Simplify the following expression: 1/[1 + 1/(1 + (1/x))]

Simplify the Expression

Please see the attached file for the fully formatted problem. (y2 + y - 12)/(y3 +9y2 + 20y)/[(y2-9)/(y2+3y2)]